How often does this extension go to the internet?

It never goes to internet. It only increases size of downloaded data when generating thumbnail logos and loading sites, whose logos are not images from headers of that sites. If image from site's header is used as site logo then size of downloaded data is not increased because opera downloads this image in any case. Additionally image caching is performed. So logos are downloaded not every time page loads but only when image cache expires (this is configurable in settings). Also to prevent loading of logos when cache expires and all speed dial thumbnails are already generated you can turn this extension off. Then turn it on shortly when adding/editing some speed dial items or reloading thumbnails.